Question

1. $4x + 2y = 8$

$y - 4 = - 2x$

Explanation:

Step1: Rearrange the second equation

From \( y - 4=-2x \), we can rewrite it as \( y=-2x + 4 \).

Step2: Substitute into the first equation

Substitute \( y=-2x + 4 \) into \( 4x + 2y = 8 \). We get \( 4x+2(-2x + 4)=8 \).

Step3: Simplify the equation

Expand the left - hand side: \( 4x-4x + 8 = 8 \). The \( 4x-4x \) cancels out, leaving \( 8 = 8 \).

This means that the two equations are dependent (they represent the same line), and there are infinitely many solutions of the form \( y=-2x + 4 \) (where \( x \) can be any real number).

Answer:

The system of equations has infinitely many solutions, and the solutions are given by the equation \( y=-2x + 4 \) (or equivalently, the two original equations represent the same line).